循环群与循环群直积的同构表示

本文运用基础代数中有关循环群、直积、同构等理论,证明了一个循环群可以用另一组循环群的直积形式来同构表示。     

Infants' cross-modal transfer from solid objects to their graphic representations

12-month-old infants were familiarized either tactually or visually with objects and then tested for visual recognition memory using either (1) the familiar and a novel object, (2) colored pictures of the objects, or (3) outline drawings of them. In Study 1, infants showed recognition memory on all 3 visual intramodal problems but showed cross-modal transfer only when objects were used as test stimuli. With increased familiarization times in Study 2, transfer from tactually presented samples to both pictorial displays was achieved, indicating that after feeling an object the infants were able to recognize it visually solely on the basis of its contour. With reduced familiarization times in Study 3, there was no evidence for transfer from visually presented samples to the 2 pictorial displays, replicating the pattern of results observed cross-modally in Study 1 and suggesting that, at least in certain respects, cross-modal and intramodal perception follow similar principles.     

Parents' representations of their children's mathematics learning in multiethnic primary schools

There is a growing concern that governmental calls for parental involvement in children's school mathematics learning have not been underpinned by research. In this article the authors aim to offer a contribution to this debate. Links between children's home and school mathematical practices have been researched in sociocultural studies, but the origins of differences within the same cultural group are not well understood. The authors have explored the notion that parents' representations of school mathematics and associated practices at home may play a part in the development of these differences. This article reports an analysis of interviews with parents of 24 children of Pakistani and White origin enrolled in primary schools in England, including high and low achievers in school mathematics. The extent to which the parents represented their own school mathematics and their child's school mathematics as the ‘same’ or ‘different’ are examined. In addition, ways in which these representations influenced how they tried to support their children's learning of school mathematics are examined. The article concludes with reflections on the implications of the study for education policy.     

对角优势矩阵及其迭代性质

本文主要讨论了对角优势矩阵的性质及其应用,并将二者作了简单的糅合。由于对角优势矩阵的非奇异性,正稳定性,且由其组成的系数方程用Jacobi和Gauss—Seidel迭代法均收敛的良性,使得对角优势矩阵在方程及矩阵中有其重要地位．     

由—迭代方程组引出的一些结论

对美国数学邀请赛9—7题的讨论已有报道．本拟给出另一种解释．原题为：     

非扩张映射不动点带误差的迭代过程

在一致凸Banach空间中对非扩张映射讨论了带误差的Mann迭代过程的一些特性,将Reich的相应定理扩展到带误差Mann的迭代过程。     

Newton迭代法的应用研究

重点讨论了求解非线性方程根的Newton迭代法,根据方程的根的重数来确定：当为单根时,使用Newton迭代法;当为重根时,使用改进法;当根的重数不确定时,使用综合法。     

由一迭代方程组引出的一些结论

对美国数学邀请赛9-7题的讨论已有报道[1].本文拟给出另一种解释.原题为:求A2,这里A是方程x=19 9119 9119 9119 9119 91x①所有根的绝对值之和.首先,方程①右边易化为Ax BCx D(C≠0)的形式,于是,方程①可化为一元二次方程x(Cx D)=Ax B.②显然,方程②在复数域C内恰有两个解.其次     

并行块SAOR迭代算法及其收敛性

推广了解线性方程组的SAOR迭代算法，给出了并行块SAOR迭代算法（简记为MBSAOR迭代法)模型，并在系数矩阵为块H—矩阵的条件下，证明了MBSAOR迭代算法的收敛定理。     

线性方程组的距离迭代解法

目前,线性方程组的数值求解,常用的方法是Gauss-Seidel迭代法.Gauss-Seidel的收敛性要求条件很强.对于一般n元方程组,如果系数矩阵的秩小于n,则Gauss-Seidel迭代一般不能使用.本文所要介绍的距离迭代法,及其改进方法,折线迭代法,对于方程组基本上没有什么要求,只要有解,就一定能够得到.距离迭代法具有鲜明的几何意义,理论、方法十分朴素易懂,速度快,精度高,是一个值得推荐的优秀数值方法.     

Preferred representations and knowledge acquisition

European Journal of Psychology of Education - There are two kinds of preferential representations. They are connected on the one hand to the degree of typicality of the instance in relation to the...     

Schematic representations in arithmetical problem solving: Analysis of their impact on grade 4 students

While the value of ‘schematic representations’ in problem solving requires no further demonstration, the way in which students should be taught how to construct these representations invariably gives rise to various debates. This study, conducted on 146 grade 4 students in Luxembourg, analyzes the effect of two types of ‘schematic representation’ (diagrams vs. schematic drawings) on the solving of arithmetical problems. The results show that the presence of schematic representations has a clear positive effect on overall student performance and that a non negligible proportion of students manage to reuse the representations encountered in order to solve new problems. While showing an effect slightly in favor of diagrams as opposed to schematic drawings, our results do not really permit us to draw any conclusions about the form that these representations should take, in particular since a differential effect was observed depending on the type of problem.     

线性递归序列与射影函数的迭代

给出了2阶实线性递归序列与1维实射影函数的迭代的关系,进而利用矩阵的幂得到2阶实线性递归序列的通项及极限性质。     

Children's insecure representations of the interparental relationship and their school adjustment: the mediating role of attention difficulties

This study examined the role of attention difficulties as a mediator of associations between children's insecure representations of the interparental relationship and their school adjustment in a sample of two hundred and sixteen 6-year-old children. Consistent with hypotheses, findings from structural equation models indicated that observer ratings of children's insecure representations of interparental relationships in a story completion task predicted computerized task assessments and parent reports of children's attention difficulties 1 year later. Children's attention difficulties, in turn, were associated with concurrent levels of school problems and increases in school problems over a 1-year period as indexed by teacher reports. Attention difficulties accounted for an average of 34% of the association between insecure internal representations and school problems.     

一类Ishikawa迭代收敛问题

使用新的逼近技巧,研究了一致光滑的Banach空间中具有Lipschitz强增生算子的带误差项的Ishikawa迭代过程的收敛性问题.     

Newton迭代的一个双侧逼近格式

本文构造求ａ的Ｎｅｗｔｏｎ迭代的一个双侧格式，讨论非线性方程组的Ｎｅｗｔｏｎ迭代的双侧逼近格式，并给出相应的两个数值计算结果的例子．它将方程的真解套在其左右两侧的一定范围内，更符合实际要求和具体的应用     

非扩张映像显式迭代序列强收敛性

在具有一致Gateaux可微范数的自反严格凸Banach空间中,利用半闭原理等基本理论,证明了非扩张映像显式迭代序列的强收敛性,完善和改进了相关的证明．     

Identities, social representations and critical thinking

This comment on L. Simonneaux and J. Simonneaux paper focuses on the role of identities in dealing with socio-scientific issues. We argue that there are two types of identities (social representations) influencing the students’ positions: On the one hand their social representations of the bears’ and wolves’ identities as belonging to particular countries (Slovenia versus France for bears, France and Italy for wolves), in other words, as having national identities; on the other hand representations of their own identities as belonging to the field of agricultural practitioners, and so sharing this socio-professional identity with shepherds and breeders, as opposed to ecologists. We discuss how these representations of identities influenced students’ reasoning and argumentation, blocking in some cases the evaluation of evidence. Implications for developing critical thinking and for dealing with SSI in the classrooms are outlined.

迭代数列的周期性

本先介绍迭代数列等有关概念,再给出三个关于迭代数列周期性的定理及若干个推论,并给以证明,最后提出一些未解决的猜想。